What is log_{2}((s^5)/(9t^2)) ?

The solution to log_{2}((s^5)/(9t^2)) is 5log_{2}(s)-2log_{2}(3)-2log_{2}(t)

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simplify log_{2}((s^5)/(9t^2))

simplify

lo g_{2} (\frac{s ^{5}}{9 t ^{2}})

5 lo g_{2} (s) - 2 lo g_{2} (3) - 2 lo g_{2} (t)

Solution steps

lo g_{2} (\frac{s ^{5}}{9 t ^{2}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (\frac{s ^{5}}{9 t ^{2}}) = lo g_{2} (s^{5}) - lo g_{2} (9 t^{2})

= lo g_{2} (s^{5}) - lo g_{2} (9 t^{2})

lo g_{2} (s^{5}) = 5 lo g_{2} (s)

lo g_{2} (9 t^{2}) = 2 lo g_{2} (3) + 2 lo g_{2} (t)

= 5 lo g_{2} (s) - (2 lo g_{2} (3) + 2 lo g_{2} (t))

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{2} (3) + 2 lo g_{2} (t)) = - 2 lo g_{2} (3) - 2 lo g_{2} (t)

= 5 lo g_{2} (s) - 2 lo g_{2} (3) - 2 lo g_{2} (t)

lo g_{9} (\frac{1}{4}) + lo g_{3} (8)

lo g_{m} (\frac{1}{3})

5 lo g_{7} (u) + 2 lo g_{7} (v)

3 lo g_{10} (x) + lo g_{10} (z) - 2 lo g_{10} (y)

What is log_{2}((s^5)/(9t^2)) ?
The solution to log_{2}((s^5)/(9t^2)) is 5log_{2}(s)-2log_{2}(3)-2log_{2}(t)